MINIMAL GEODESICS ON GL(n) FOR LEFT-INVARIANT, RIGHT-O(n)-INVARIANT RIEMANNIAN METRICS

被引：8

作者：

Martin, Robert J. ^{[1
]}

Neff, Patrizio ^{[1
]}

机构：

[1] Univ Duisburg Essen, Lehrstuhl Nichtlineare Anal & Modellierung, Fak Math, Thea Leymann Str 9, D-45127 Essen, Germany

来源：

JOURNAL OF GEOMETRIC MECHANICS | 2016年 / 8卷 / 03期

关键词：

Geodesics; geodesic distance; general linear group; left-invariance; isotropy; STRAIN MEASURES; MINIMIZATION; PROPERTY; GEOMETRY;

D O I：

10.3934/jgm.2016010

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We provide an easy approach to the geodesic distance on the general linear group GL(n) for left-invariant Riemannian metrics which are also right-O(n)-invariant. The parameterization of geodesic curves and the global existence of length minimizing geodesics are deduced using simple methods based on the calculus of variations and classical analysis only. The geodesic distance is discussed for some special cases and applications towards the theory of nonlinear elasticity are indicated.

引用

页码：323 / 357

页数：35

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